vertex form of a quadratic function
A quadratic function written in the form f(x)=a(x-h)^2+k, where a is not equal to 0 and where a, h, and k are constants and (h,k) is the vertex.
The vertex form of a quadratic function is written as:
f(x) = a(x – h)^2 + k
Where a is the coefficient of the quadratic term, and h and k are the coordinates of the vertex. The values of a, h, and k can be obtained from the standard form of a quadratic equation:
f(x) = ax^2 + bx + c
To convert a quadratic function in standard form to vertex form, we complete the square as follows:
f(x) = a(x^2 + bx/a) + c
f(x) = a(x^2 + bx/a + (b/2a)^2 – (b/2a)^2) + c
f(x) = a(x + b/2a)^2 – (b/2a)^2 + c
The value of a remains the same in vertex form as in standard form. The vertex is located at the point (-b/2a, -b^2/4a + c).
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